I have 2 heelers. I recently have taken on more hours at work and am not home as much as I used to be. I have fenced off a long area of my yard and keep my dogs there when I am at work because they totally destroyed my landscape and yard in a matter of 2 days. I have bermuda grass which gets traumatized if you walk on it a couple of times. Needless to say, the grass in their area has died and now they are in mostly dirt or mud pit whenever it rains even a little bit. I feel this can't be healthy.
Is their a kind of grass that can withstand their stampeding that won't look bad if it spreads to the rest of my yard? Also, should I be treating their area with anything special? I always pick up the poop, but they still urinate in there.

You might be better off putting down about three inches of mulch in the dog run. Your city probably sells it by the trailer load very cheap. If the dog run is getting muddy, you might have a drainage problem and may have to put in a drainage system like french drain or J-drain.

I agree with mulching a dog run.